Unfortunately, there's not much you can do in this circumstance; it's a problem that most aging 6930's see, and HP has since made design changes to improve the latching mechanism.
You could try replacing the base cover with a newer one, as that assembly should be included, or try bending the spring-pushed latching bar to have a better grip. Both require a considerable amount of work, tearing the machine down to it's core, and aren't guaranteed to resolve the problem.
The new LCDs have thinner clips that latch easier, and the internal latch bar is metal instead of plastic.
I, sadly, had to replace the base cover on about 2000 machines in 2009-2010.